where \(\rm {norm}(.)\)  is \(\ell _2\)  normalization operator.
Intuitively, one can see \(\tilde{\mathbf {x}}_i\)  as the common object representation
within the \(i\) -th image which is estimated by computing the weighted average
over all the proposals where the contribution of proposals are controlled by
their soft labels. Given \(\tilde{\mathbf {x}}_i\) , the novel class direction \({\mathbf {\theta }}\)  is
estimated as the mean of the common object representations similar to the
prototypical networks [1]}. Finally, the estimated
mean is projected back onto the unit hypersphere.
